Applying the classical work of Nakayama [Ann. of Math. 40 (1939)], we exhibit a general form of non-Frobenius self-injective finite-dimensional algebras over a field.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm105-1-12, author = {Andrzej Skowro\'nski and Kunio Yamagata}, title = {A general form of non-Frobenius self-injective algebras}, journal = {Colloquium Mathematicae}, volume = {106}, year = {2006}, pages = {135-141}, zbl = {1148.16016}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm105-1-12} }
Andrzej Skowroński; Kunio Yamagata. A general form of non-Frobenius self-injective algebras. Colloquium Mathematicae, Tome 106 (2006) pp. 135-141. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm105-1-12/